Chapter 8 - Kinetics

The primary function of enzymes is to accelerate reaction rates, or the ____ of reactions

Velocities

What does a kinetic description allow us to quantify with enzymes?

1. How fast an enzyme can operate (Substrate → Product)

2. How fast it operates at the substrate concentrations found in a cell

3. What substrate is most readily operated on by the enzyme

(T/F) Metabolism in the cell is done via a complex array of dozens of metabolic pathways composed of thousands of different reactions

True

Michaelis-Menten Enzyme

Enzymes that do generally lack sophisticated regulatory properties

Allosteric enzymes

Act as both catalysts and information sensors that sense signals in the environment, of which allows them to adjust the rate of their reactions to meet the cell’s needs

• Allows for efficient coordination of the cell’s pathways

• Have quarternary structures with muiltiple active sites in each enzyme

• More complex kinetics than michaelis-menten

Kinetics

The study of the rates of chemical reactions

Enzyme Kinetics

The study of the rates of enzyme-catalyzed reactions

Explain the formula: V = -d[A]/dt = d[P]/dt for the reaction A → P

The velocity of a reaction (V) is the amount of A that disappears (equivalently, the amount of P that appears) in a given time.

Explain the formula: V = k[A]

The velocity of the reaction (V) is directly related to the concentration of A by a proportionality constant called the rate constant (k)

First-order reactions and how they affect V = k[A]

Velocity is directlky proportional to reactant concentration; k has units of s^-1

Second-order reactions and how they affect V = k[A]

Bimolecular reactions with two reactants; k has units of M^-1s^-1

What is the initial velocity (V₀) of catalysis? What does it vary depend on?

Defined as the number of moles of product formed per second shortly after the reaction has begun

• Varies with the substrate concentration [S] when enzyme concentration is held constant

(T/F) Enzyme concentrations fluxuate drastically in cells

False. They are held relatively constant.

Explain what k₁ means in the following reaction

The rate constant for the formation of the enzyme-substrate (ES) complex

Explain what k₂ means in the following reaction

The rate constant for the formation of the product (P)

Explain what k_-1 and k_-2 means in the following reaction

The constants for the respective reverse reactions

What is this chart displaying?

• At low [S], the rate rises linearly with substrate concentration

• At higher [S], the rate levels off and approaches maximum

Why is it most useful to focus on the intial rate of enzyme kinetics?

1. The rate of the reaction (the slope of the tangent line in the figure) decreases over time

2. Only at the beginning of the reaction is the exact concentration of substrate known

   1. The reverse reaction is negligible at this point

Michaelis-Menten equation

Describes how enzyme activity varies with substrate concentration

Michaelis constant (K_M)

A measure of enzyme efficiency

• Unique to each enzyme

• Idependent of enzyme concentration

• Depends on the particular substrate

• Depends on environmental conditions (pH, temp, ionic strength)

• Describes the properties of the enzyme-substrate interaction

• Varies for enzymes that can use different substrates

  • Provides a measurement of the substrate concentration required for significant catalysis to take place

Maximum Velocity (V_max)

• Can be attained only when all of the total enzyme (E_T) is bound to substrate (S)

• Directly dependent on enzyme concentration

At very low substrate concentrations (when S is much less than K_M), what happens to the velocity?

It is directly proportional to [S] concentration

At very high substrate concentrations (when S is much greater than K_M), what happens to the velocity?

Velocity is maximimal and independent of [S] concentration

What happens when an enzyme is operating at V_max?

• All of the available enzyme is bound to substrate

• The additiojn of more substrate does not affect the velocity of the reaction

• The enzyme is displaying zero-order kinetics

• The enzyme is said to be saturated

When V₀ = V_max/2, what does this mean for K_M?

It its equal to the substrate concentration at which the rx velocity is half its maximal value

Michaelis-Menten enzymes

Simple, monomeric, and unregulated enzymes free to evolve to become as fast and as efficient as possible

• Governed by mass action

Mass action

Enzymes in which, if a substrate is present, they will catalyse

Lineweaver-Burk plot

Also called a double-reciprocal plot

• Plots out 1/V₀ vs 1/[S]

• Can determine K_M and V_max

What does the slope of a Lineweaver-Burk plot represent?

K_M/V_max

What does the y-intercept of a Lineweaver-Burk plot represent?

-1/V_max

What does the x-intercept of a Lineweaver-Burk plot represent?

-1/K_M

Elasticity

Refers to an enzyme’s activity being sensitive to changes in environmental conditons

• Ability for the enzyme to adapt

At substrate values below K_M, what is an enzymes elasticity?

It will be very sensitive to changes in substrate concentration and display little activity

At substrate values well above K_M, what is an enzymes elasticity?

It will have greater catalytic activity but be insensitive to changes in substrate concentration

• Max activity

At substrate values approximately K_M, what is an enzymes elasticity?

It will have significant activity (1/2 V_max) but still sensitive to changes in substrate concentration

Turnover number (k_cat) and what other property can reveal it

The number of substrate molecules that an enzyme can convert into product per unit time when fully saturated

• V_max reveals this number if the concentration of active sites [E]_T is known

  • k_cat = V_max/[E]_T

Specificity Constant

The rate constant for the interaction of substrate and enzyme when [S] is much less than K_M

• A measure of catalytic efficiency

  • Takes into account both the rate of catalysis with a particular substrate and the nature of the enzyme-substrate interaction

Bisubstrate reactions

Start with two substrates and yield two products

Sequential reactions

A type of bisubstrate reaction where all substrates must bind to the enzyme before any product is released

• Forms a ternary complex (enzyme + both substrates)

• Binding may be ordered (substrates bind the enzyme in a defined sequence) or random

Double-Displacement Reactions

A type of bisubstrate reaction where one or more products are released before all substrates bind the enzyme

• Defining feature is a substituted enzyme intermediate in which the enzyme is temporarily modified

• The substrates and products appear to bounce on and off the enzyme like a ping-pong ball bounces on and off a table

Allosteric enzymes typically catalyze the ___ step of metabolic pathways

Committed

Feedback inhibition

For allosteric enzymes, where the pathway itself is regulated by the pathway’s own products

Feedback inhibitors

• Bear no strucutral resemblance to the substrate or the product of the enzyme they inhibit

• Usually do not bind at the active site, but rather at a distinct regulatory site on the allosteric enzyme

  • Hence their name “allosteric”: they are regulated by molecules binding elswhere

In this chart, what products are inhibiting what enzymes?

• F is inhibiting e₁

• I is inhibiting e₁₀

• K is inhibiting e₁ and e₁₀

In this chart, what products are stimulating what enzymes?

• F is stimulating e₁₀

• I is stimulating e₁

What, overall, is this chart conveying?

The process iof allosteric enzyme regulation

• F and I make K.

  • If more F is made than I:

    • F can inhibit e₁, stopping the eventual creation of F

    • F can stimulate e₁₀, increasing up the eventual creation of I

      • Both help put F and I into equal balance with one another so neither is wasted

What shape do allosteric enzymes make on a graph? Why?

Sigmoidal

• Due to the fact that they respond to substrate as well as regulators, unlike Michaelis-Menten whom responds solely to substrate

• A sharp rise in V₀ occurs in the middle of the curve rather than immediately

Concerted Model for Allosteric Enzymes (allostery)

Allosteric enzymes usually have multiple active sites on different polypeptide chains

• Two states: relaxed (R) and tense (T); T is significantly less active but more stable

• Equilibrium: Without substrate or signal molecules, R and T are in equilibrium and T is predominants.

• Symmetry: all subunits must be in the same state (all T or all R, no hybrids)

• Substrate preference: S binds more readily to R than T

Allosteric Constant (L₀)

Associated with the concerted model for allostery, the T/R ratio

• Normally in the hundreds for a typical allosteric enzyme

Threshold Effect

The activity of allosteric enzymes is more sensitive to changes in subtrate concentration than are Michaelis-Menten enzymes with the same V_max

• Allosteric enzymes transition from a less active state to a more active state within a narrow range of substrate concentration

• Like an on/off switch, cooperativity ensures most of the enzyme is either on (R) or off (T)

Positive Effectors

Bind to the R form at a regulatory site of an allosteric enzyme and stabilize it

• Increase concentration of R

• Makes R and S interaction more likely

• Lowers the threshold concentration of substrate needed for activity

• Blue in the picture

Negative Effectors

Bind to the T form of an allosteric enzyme and stabilize it

• Increased concentration of T, decreasing the likelihood of an R binding to an S

• Raise the threshold concentration of substrate needed for activity

• Red in the picture

Heterotropic effects

The effects of regulatory molecules on allosteric enzymes are referred to as heterotropic effects because the binding of one molecule (the effector) has an effect on a different molecule (the substrate)

• Shift the sigmoidal curve to the left (activators) or right (inhibitors)

Homotropic effects

If the effects are due to molecules of the same kind, like substrates binding to different subunits, these effects referred to as homotropic effects because they are due to the binding of more than one of the same molecules

Sequential Model for Allosteric Enzymes (allostery)

More readily accommodates negative cooperativity, where the binding of one substrate decreases the affinity of other sites

Which model do allosteric enzymes follow?

A mixture of sequential and concerted

Ensemble Studies

Most experiments use an enzyme preparation in a solution; even a few microliters hold millions of enzymes

• Assumes all enzyme molecules are the same or very similar

  • Generates a single value representing the averge enzyme activity for a heterogeneous assembly

Single-Molecule Experiments

Examine one enzyme molecule at a time. Yield great information:

• Existence of rare or transient structures

• Fleeting events in a reaction sequence

• Mechanical forces affecting or generated by an enzyme